WASHINGTON (AP) — An ambitious, bipartisan effort to overhaul the military justice system and stanch the increasing number of sexual assaults gained crucial support from conservatives Tuesday, setting up a showdown with the Pentagon’s top brass.

Sen. Rand Paul, R-Ky., announced his backing for legislation sponsored by Sen. Kirsten Gillibrand, D-N.Y., that would remove commanders from the process of deciding whether serious crimes, including sexual misconduct cases, go to trial. That judgment would rest instead with seasoned trial lawyers who have prosecutorial experience and hold the rank of colonel or above.

“There’s no reason why conservatives shouldn’t support this,” Paul told reporters at a Capitol Hill news conference with other Republicans and Democrats who support the measure.

A third of the Senate — 33 lawmakers — favor Gillibrand’s effort that she will try to attach to a sweeping defense policy bill, perhaps as soon as this month. She faces opposition from Senate Armed Services Committee Chairman Carl Levin, D-Mich., who — echoing the Joint Chiefs of Staff — wants to keep commanders involved in deciding whether to prosecute sexual assault cases.

“If you remove the chain of command, you are taking away the club that they need to change the culture,” Levin told reporters Tuesday at a breakfast discussion hosted by The Christian Science Monitor. The club, he said, is the ability of commanders to prosecute people.

“It’s commanders who make it work,” he said. “They give orders.”

Military leaders have argued that removing the decision from their purview would undercut the ability of officers to maintain good order and discipline in their units.

The Pentagon estimated in a recent report that as many as 26,000 military members may have been sexually assaulted last year, up from an estimated 19,000 assaults in 2011, based on an anonymous survey of military personnel. While the number of sexual assaults that members of the military actually reported rose 6 percent to 3,374 in 2012, thousands of victims were still unwilling to come forward despite new oversight and assistance programs aimed at curbing the crimes, the report said.

Backers of Gillibrand’s legislation insisted that leaving the decisions with the commanders has failed to stop a crisis within the military ranks.

“The status quo is not working and we need to shake it up,” said Sen. Charles Grassley, R-Iowa.

Democratic Sen. Barbara Boxer, D-Calif., displayed a chart with quotes from defense secretaries past and present — from Dick Cheney in the early 1990s to Chuck Hagel today — saying the military has zero tolerance for sexual assault.

“It’s enough with the words. It’s enough with the empty promises,” Boxer said.

Without specifically commenting on Gillibrand’s bill, White House spokesman Jay Carney said the Obama administration would weigh any ideas for improving the military justice system.

“We are open to consideration of any ideas, and that includes proposed legislation, and we will work with Congress and we will work with the Department of Defense on ways to deal with and improve the prosecution and prevention and victim support when it comes to sex assault in the military,” Carney told reporters.

Last month, in a closely watched vote, the Armed Services Committee backed a Levin bill designed to increase pressure on senior commanders to prosecute sexual assault cases by requiring a top-level review if they fail to do so. Levin’s proposal also would make it a crime to retaliate against victims who report a sexual assault and also calls on the Pentagon to relieve commanders who fail to create a climate receptive for victims.

The measure passed 17-9. Gillibrand, who heads the committee’s personnel subcommittee, had the support of several Democrats and Republicans for her effort, including Sens. Ted Cruz of Texas and David Vitter of Louisiana. The full committee, however, rebuffed her approach.

Cruz told reporters at the news conference that victims often are unwilling to report crimes because they have to tell their bosses. He pointed out that several allies with professional militaries have already taken the decision out of the chain of command.

In fact, Boxer displayed a chart that showed that Israel did it in 1955, Canada in 1998, Australia in 2005 and the United Kingdom in 2006.